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Abstract:

The present invention relates to a method for producing a silica glass
substrate for an imprint mold, containing: obtaining a glass body from a
glass-forming raw material containing an SiO2 precursor; machining
the glass body into a glass substrate having a predetermined shape; and
removing an affected layer on a surface of the glass substrate, to
produce a silica glass substrate for an imprint mold having a fictive
temperature distribution in a region from the surface to a depth of 10
μm on the side to be subjected to a transfer pattern formation of the
glass substrate being within ±30° C.

Claims:

1. A method for producing a silica glass substrate for an imprint mold,
comprising: obtaining a glass body from a glass-forming raw material
containing an SiO2 precursor; machining said glass body into a glass
substrate having a predetermined shape; and removing an affected layer on
a surface of said glass substrate, to produce a silica glass substrate
for an imprint mold having a fictive temperature distribution in a region
from the surface to a depth of 10 μm on the side to be subjected to a
transfer pattern formation of said glass substrate being within
.+-.30.degree. C.

2. The method for producing a silica glass substrate for an imprint mold
according to claim 1, wherein the removal of said affected layer is
performed by an etching treatment.

3. The method for producing a silica glass substrate for an imprint mold
according to claim 2, wherein said glass substrate surface is subjected
to the etching treatment to remove a region from the surface to a depth
of 100 nm or more of said glass substrate.

4. The method for producing a silica glass substrate for an imprint mold
according to claim 1, wherein said glass body is obtained by a process
comprising the following steps (a) to (e): (a) a step of depositing a
glass fine particle obtained from the glass-forming raw material
containing an SiO2 precursor by a soot process to obtain a porous
glass body, (b) a step of heating said porous glass body to a
densification temperature to obtain a dense body, (c) a step of heating
said dense body to a transparent vitrification temperature to obtain a
transparent glass body, (d) a step of, if desired, heating said
transparent glass body to a softening point or higher and molding to
obtain a molded glass body, and (e) a step of annealing the transparent
glass body obtained in said step (c) or the molded glass body obtained in
said step (d).

5. The method for producing a silica glass substrate for an imprint mold
according to claim 1, wherein said glass-forming raw material further
contains a TiO2 precursor.

6. The method for producing a silica glass substrate for an imprint mold
according to claim 2, wherein said etching treatment contains a process
of immersion in a fluorine-containing chemical solution.

7. A method for producing an imprint mold, comprising forming a transfer
pattern through etching on a surface of the silica glass substrate for an
imprint mold obtained by the production method according to claim 1.

Description:

TECHNICAL FIELD

[0001] The present invention relates to a method for producing a
silica-based glass substrate for an imprint mold, and a method for
producing an imprint mold.

BACKGROUND ART

[0002] As a method for forming a fine concave-convex pattern with a
dimension of 1 nm to 10 μm on a surface of various substrates (for
example, a single crystal substrate such as Si and sapphire, and an
amorphous substrate such as glass) in a semiconductor device, an optical
waveguide, a micro-optical element (such as diffraction grating), a
biochip, a microreactor or the like, imprint lithography of pressing an
imprint mold having on a surface thereof a reversed pattern (transfer
pattern) of a concave-convex pattern against a curable resin layer formed
on a substrate surface and curing the curable resin layer to form the
concave-convex pattern on the substrate surface is attracting attention.

[0003] According to the imprint lithography, a fine concave-convex pattern
can be formed on a substrate surface at a low cost compared with
conventional methods.

[0004] The imprint lithography includes photo-imprint lithography of
curing a photocurable resin by irradiating the resin with light (e.g.,
ultraviolet ray), and heat-cycle imprint lithography of curing a
thermosetting resin by heating the resin.

[0005] The imprint mold for the photo-imprint lithography is required to
have light transmittance, chemical resistance and dimensional stability
against temperature rise due to irradiation with light.

[0006] The imprint mold for the heat-cycle imprint lithography is required
to have chemical resistance, and dimensional stability during heating.

[0007] As a substrate for an imprint mold, in view of light transmittance
and chemical resistance, a silica glass is often used. However, the
silica glass lacks dimensional stability, because its thermal expansion
coefficient near room temperature is as high as about 500 ppb/° C.

[0008] As regards a silica-based glass having a low thermal expansion
coefficient, for example, the following has been proposed:

[0009] (1) silica•titania glass for a nanoimprint stamper,
containing titania of from 2 mass % or more and 15 mass % or less, and a
linear expansion coefficient in the temperature range of 20° C. to
35° C. being within the range of ±200 ppb/° C. (see,
Patent Document 1).

[0010] However, there is a problem that when a transfer pattern is formed
on a surface of the silica•titania glass of (1) by etching,
dimensional accuracy of the transfer pattern is reduced. This problem is
caused because the silica•titania glass of (1) has a variation in
the titania concentration in the glass and the etching rate is increased
in the portion having a high titania concentration.

[0011] In the case of forming a fine concave-convex pattern with a
dimension of 1 nm to 10 μm by imprint lithography, it is required to
reduce a variation in dimension of the concave-convex pattern to ±10%
or less, preferably ±5% or less. Accordingly, the substrate for an
imprint mold is required to reduce a variation in dimension of the
transfer pattern formed by etching to ±10% or less, preferably ±5%
or less.

[0012] As regards a substrate for an imprint mold, on which a transfer
pattern with high dimensional accuracy can be formed, for example, the
following has been proposed:

[0013] (2) a TiO2-containing silica glass substrate, having a thermal
expansion coefficient at 15° C. to 35° C. being within
±200 ppb/° C., a TiO2 concentration of from 4 to 9 wt %,
and a TiO2 concentration distribution in the surface to be subject
to formation of a transfer pattern thereon being within ±1 wt %
(Patent Document 2).

[0014] However, in the TiO2-containing silica glass substrate of (2),
even when the TiO2 concentration distribution in the surface is
within ±1 wt %, the variation in dimension of the transfer pattern
sometimes exceeds ±10%.

[0015] Incidentally, Patent Document 2 discloses that since the etching
rate depends also on a fictive temperature distribution in the surface of
the TiO2-containing silica glass substrate, the fictive temperature
distribution in the substrate surface is preferably controlled to be as
narrow as possible (paragraphs [0022] and [0023] of Patent Document 2);
and for controlling the fictive temperature distribution in the substrate
surface to fall within ±100° C., formed TiO2--SiO2
glass body is annealed under specific conditions (paragraph [0035] of
Patent Document 2).

[0016] However, even when the formed TiO2--SiO2 glass body is
annealed under the specific conditions, in the substrate for an imprint
mold obtained from the glass body, a variation in etching rate on the
surface occurs. Thus, the dimensional accuracy of the transfer pattern is
not yet satisfied.

[0019] The present invention provides a method for producing a
silica-based glass substrate for an imprint mold, on which a transfer
pattern with high dimensional accuracy can be stably formed, and a method
for producing an imprint mold having a transfer pattern with high
dimensional accuracy.

Means for Solving the Problems

[0020] The present invention provides a method for producing a silica
glass substrate for an imprint mold, containing: obtaining a glass body
from a glass-forming raw material containing an SiO2 precursor;
machining the glass body into a glass substrate having a predetermined
shape; and removing an affected layer on a surface of the glass
substrate, to produce a silica glass substrate for an imprint mold having
a fictive temperature distribution in a region from the surface to a
depth of 10 μm on the side to be subjected to a transfer pattern
formation of the glass substrate being within ±30° C.

[0021] In the method for producing a silica glass substrate for an imprint
mold according to the present invention, it is preferred that the removal
of the affected layer is performed by an etching treatment.

[0022] In the method for producing a silica glass substrate for an imprint
mold according to the present invention, it is preferred that the glass
substrate surface is subjected to the etching treatment to remove a
region from the surface to a depth of 100 nm or more of the glass
substrate.

[0023] In the method for producing a silica glass substrate for an imprint
mold according to the present invention, it is preferred that the glass
body is obtained by a process comprising the following steps (a) to (e):

[0024] (a) a step of depositing a glass fine particle obtained from the
glass-forming raw material containing an SiO2 precursor by a soot
process to obtain a porous glass body,

[0025] (b) a step of heating the porous glass body to a densification
temperature to obtain a dense body,

[0026] (c) a step of heating the dense body to a transparent vitrification
temperature to obtain a transparent glass body,

[0027] (d) a step of, if desired, heating the transparent glass body to a
softening point or higher and molding to obtain a molded glass body, and
(e) a step of annealing the transparent glass body obtained in said step
(c) or the molded glass body obtained in said step (d).

[0029] In the method for producing a silica glass substrate for an imprint
mold according to the present invention, it is preferred that the etching
treatment contains a process of immersion in a fluorine-containing
chemical solution.

[0030] Further, the present invention provides a method for producing an
imprint mold, comprising forming a transfer pattern through etching on a
surface of the silica glass substrate for an imprint mold obtained by the
production method of the present invention.

Advantage of the Invention

[0031] According to the method for producing a silica-based glass
substrate for an imprint mold of the present invention, a silica-based
glass substrate for an imprint mold, on which a transfer pattern with
high dimensional accuracy can be stably formed, can be easily produced.

[0032] According to the method for producing an imprint mold of the
present invention, an imprint mold having a transfer pattern with high
dimensional accuracy can be easily produced.

MODE FOR CARRYING OUT THE INVENTION

Method for Producing Silica-Based Glass Substrate for Imprint Mold

[0033] The method for producing a silica-based glass substrate of the
present invention is a method comprising: obtaining a glass body from a
glass-forming raw material containing an SiO2 precursor; machining
the glass body into a glass substrate having a predetermined shape; and
removing an affected layer on a surface of the glass substrate, to
produce a silica glass substrate for an imprint mold, having a fictive
temperature distribution in a region from the surface to a depth of 10
μm on the side to be subjected to a transfer pattern formation of the
glass substrate is within ±30° C.

[0034] The present inventors have found that variation in etching rate on
a surface of a silica glass substrate for an imprint mold, which affects
dimensional accuracy of a transfer pattern, is attributable to an
affected layer produced by machining such as cutting, shaving and
polishing. That is, even when a glass substrate having a small fictive
temperature distribution, for example, as in Patent Document 2 is
prepared, if an affected layer is produced by polishing, a variation
occurs in etching rate on the surface, and the dimensional accuracy of a
transfer pattern is impaired. In the present invention, the affected
layer indicates a region which is present in the surface produced by
machining such as cutting, shaving and polishing and in which the etching
rate becomes higher by 10% or more than that in the inside at a depth of
10 μm or more from the surface. The thickness of the affected layer is
within several μm, usually within 1 μm, from the surface. The
difference in etching rate between the surface and the inside is also
produced by occurrence of a change in fictive temperature of the surface.
However, the region having a different fictive temperature produced in
the surface due to a heat treatment or the like is deeper than the
affected layer above and gradually changed in the fictive temperature and
therefore, is differentiated from the affected layer.

[0035] In the present invention, the silica-based glass means a silica
(SiO2) glass or a silica (SiO2) glass containing TiO2,
B2O3, F, SnO2 or the like as a dopant. In the silica-based
glass, SiO2 content is preferably 88 mass % or more. In the
description of the present invention, the silica-based glass is sometimes
simply referred to as a silica glass.

[0036] A specific example of the method for producing a silica-based glass
substrate of the present invention is described in detail below by
taking, as an example, the case where the silica-based glass is a
TiO2--SiO2 glass.

[0037] The method for producing a TiO2--SiO2 glass substrate for
an imprint mold (hereinafter, referred to as a TiO2--SiO2 glass
substrate) includes a method containing the following steps (a) to (g):

[0038] (a) a step of depositing a TiO2--SiO2 glass fine particle
obtained from a glass-forming raw material containing an SiO2
precursor and a TiO2 precursor by a soot process to obtain a porous
TiO2--SiO2 glass body,

[0039] (b) a step of heating the porous TiO2--SiO2 glass body to
the densification temperature to obtain a TiO2--SiO2 dense
body,

[0040] (c) a step of heating the TiO2--SiO2 dense body to the
transparent vitrification temperature to obtain a transparent
TiO2--SiO2 glass body,

[0041] (d) a step of, if desired, heating the transparent
TiO2--SiO2 glass body to a softening point or higher and
molding to obtain a molded TiO2--SiO2 glass body,

[0042] (e) a step of annealing the transparent TiO2--SiO2 glass
body obtained in the step (c) or the molded TiO2--SiO2 glass
body obtained in the step (d),

[0043] (f) a step of subjecting the annealed TiO2--SiO2 glass
body obtained in the step (e) to machining such as cutting, shaving and
polishing to obtain a TiO2--SiO2 glass substrate having a
predetermined shape, and

[0044] (g) a step of removing the affected layer on the surface of the
TiO2--SiO2 glass substrate having a predetermined shape
obtained in the step (f) to obtain a TiO2--SiO2 glass
substrate.

(Step (a))

[0045] A TiO2--SiO2 glass fine particle (soot) obtained by flame
hydrolysis or thermal decomposition of a SiO2 precursor and a
TiO2 precursor each serving as a glass-forming raw material is
deposited and grown on a substrate for deposition by a soot process,
whereby a porous TiO2--SiO2 glass body is formed.

[0046] Examples of the soot process include an MCVD (Modified Chemical
Vapor Deposition) process, an OVD (Outside Vapor Deposition) process and
a VAD (Vapor Axial Deposition) process. The VAD process is preferred from
the standpoint that, for example, the mass productivity is excellent and
a glass body having a uniform composition in a large-area plane can be
obtained by adjusting the production conditions such as size of the
deposition substrate.

[0047] The glass-forming raw material includes a gasifiable raw material.

[0048] The SiO2 precursor includes a silicon halide compound and an
alkoxysilane.

[0049] The TiO2 precursor includes a titanium halide compound and an
alkoxytitanium.

[0051] The alkoxysilane includes a compound represented by the following
formula (1):

RnSi(OR)4-n (1)

wherein R is an alkyl group having a carbon number of 1 to 4, n is an
integer of 0 to 3, and when a plurality of Rs are present, a part of Rs
may be different.

[0052] Examples of the titanium halide compound include TiCla and
TiBr4.

[0053] The alkoxytitanium includes a compound represented by the following
formula (2):

RnTi(OR)4-n (2)

wherein R is an alkyl group having a carbon number of 1 to 4, n is an
integer of 0 to 3, and when a plurality of Rs are present, a part of Rs
may be different.

[0054] As the SiO2 precursor and the TiO2 precursor, a compound
containing Si and Ti, such as silicon titanium double alkoxide, may be
used.

[0055] The substrate for deposition includes a silica glass-made seed rod
(for example, the seed rod described in JP-B-63-24937). The shape is not
limited to a rod form, and a plate-shaped substrate for deposition may be
also used.

(Step (b))

[0056] The porous TiO2--SiO2 glass body obtained in the step (a)
is heated to the densification temperature in an inert gas atmosphere or
a reduced pressure atmosphere to obtain a TiO2--SiO2 dense
body.

[0057] The densification temperature means a temperature at which a porous
glass body can be densified to such an extent that a void cannot be
observed by an optical microscope.

[0058] The densification temperature is preferably from 1,250 to
1,550° C., and more preferably from 1,350 to 1,450° C.

[0059] The inert gas is preferably helium.

[0060] The pressure in the atmosphere is preferably from 10,000 to 200,000
Pa. In the present description, Pa means not a gauge pressure but an
absolute pressure. In the case of reduced pressure, the pressure is
preferably 13,000 Pa or lower.

[0061] In the step (b), it is preferred that the porous
TiO2--SiO2 glass body is placed under reduced pressure
(preferably 13,000 Pa or lower, and more preferably 1,300 Pa or lower)
and then, an inert gas is introduced to create an inert gas atmosphere of
a predetermined pressure, because homogeneity of the TiO2--SiO2
dense body is increased.

[0062] Also, in the step (b), it is preferred that the porous
TiO2--SiO2 glass body is held in an inert gas atmosphere at
room temperature or a temperature lower than the densification
temperature and then, the temperature is raised to the densification
temperature, because homogeneity of the TiO2--SiO2 dense body
is increased. In this case, the holding time is preferably 2 hours or
more.

[0063] In the case of incorporating F, for example, the following step may
be provided before the step (b).

(Step (b'))

[0064] The porous TiO2--SiO2 glass body obtained in the step (a)
is held in a reaction vessel where elemental fluorine (F2) or a
mixed gas obtained by diluting elemental fluorine (F2) with an inert
gas is filled and a solid metal fluoride is present, whereby a
fluorine-containing porous glass body is obtained. The solid metal
fluoride used is not particularly limited but is preferably a solid metal
fluoride selected from the group consisting of fluoride of an alkali
metal, fluoride of an alkaline earth metal and a mixture thereof, and
more preferably sodium fluoride. The shape of the solid metal fluoride is
not particularly limited, and an arbitrary shape suitable for arrangement
in the reaction vessel may be selected.

[0065] Alternatively, the porous TiO2--SiO2 glass body obtained
in the step (a) is held at a temperature at the densification temperature
or lower in a fluorine-containing gas atmosphere, whereby a
fluorine-containing porous TiO2--SiO2 glass body is obtained.
The fluorine-containing gas atmosphere is preferably an inert gas
atmosphere containing from 0.1 to 100 vol % of a fluorine-containing gas
(e.g., SiF4, SF6, CHF3, CF4, C2F6,
C3F8). It is preferred to perform the treatment in such an
atmosphere under a pressure of 10,000 to 200,000 Pa for from several tens
of minutes to several hours at the above-described high temperature of
the densification temperature or lower.

(Step (c))

[0066] The TiO2--SiO2 dense body obtained in the step (b) is
heated to the transparent vitrification temperature to obtain a
transparent TiO2--SiO2 glass body.

[0067] The transparent vitrification temperature means a temperature at
which a crystal cannot be observed by an optical microscope and a
transparent glass is obtained.

[0068] The transparent vitrification temperature is preferably from 1,350
to 1,750° C., and more preferably from 1,400 to 1,700° C.

[0069] The atmosphere is preferably an atmosphere of 100% inert gas (e.g.,
helium, argon), or an atmosphere containing the inert gas (e.g., helium,
argon) as a main component.

[0070] The pressure of the atmosphere is preferably reduced pressure or
normal pressure. In the case of reduced pressure, the pressure is
preferably 13,000 Pa or lower.

(Step (d))

[0071] The transparent TiO2--SiO2 glass body obtained in the
step (c) is put in a mold and heated to a temperature of the softening
point or higher, thereby molded into a desired shape to obtain a molded
TiO2--SiO2 glass body.

[0072] The molding temperature is preferably from 1,500 to 1,800°
C. When the molding temperature is 1,500° C. or higher, the
transparent TiO2--SiO2 glass body is reduced in the viscosity
and easily deformed due to its own weight. Also, growth of cristobalite
that is a crystal phase of SiO2, or growth of rutile or anatase that
are a crystal phase of TiO2, is suppressed, and so-called
devitrification hardly occurs. When the molding temperature is
1,800° C. or lower, sublimation of SiO2 is suppressed.

[0073] As for the inert gas, an atmosphere of 100% inert gas (e.g.,
helium, argon), or an atmosphere containing the inert gas (e.g., helium,
argon) as a main component is preferred.

[0074] The pressure of the atmosphere is preferably from 10,000 to 200,000
Pa.

[0075] The step (d) may be repeated a plurality of times. For example,
two-stage molding may be performed such that after the transparent
TiO2--SiO2 glass body is put in a mold and heated to a
temperature of the softening point or higher, the molded
TiO2--SiO2 glass body obtained is put in another mold and again
heated to a temperature of the softening point or higher.

[0076] Also, the step (c) and the step (d) may be performed sequentially
or simultaneously.

[0077] In the case where the transparent TiO2--SiO2 glass body
obtained in the step (c) is sufficiently large, a molded
TiO2--SiO2 glass body may be obtained by cutting the
transparent TiO2--SiO2 glass body obtained in the step (c) into
a predetermined shape without performing the subsequent step (d).

[0078] The following step (d') may be performed before the step (e).

(Step (d'))

[0079] This is a step of heating the transparent TiO2--SiO2
glass body obtained in the step (c) or the molded TiO2--SiO2
glass body obtained in the step (d) at a temperature of
T1+400° C. or higher for 20 hours or more.

[0080] T1 is the annealing point (° C.) of the
TiO2--SiO2 glass body obtained in the step (e). The annealing
point means a temperature at which the viscosity η of a glass becomes
1013 dPas. The annealing point is determined as follows.

[0081] The viscosity of a glass is measured by a beam bending method in
accordance with JIS R 3103-2:2001, and the temperature at which the
viscosity n becomes 1013 dPas is defined as the annealing point.

[0082] By performing the step (d'), striae in the TiO2--SiO2
glass body are reduced.

[0083] The "striae" indicates a compositional non-uniformity (composition
distribution) in the TiO2--SiO2 glass body. In the
TiO2--SiO2 glass body having striae, sites differing in the
TiO2 concentration are present. A site with a high TiO2
concentration has a negative coefficient of thermal expansion (CTE) and
therefore, the site with a high TiO2 concentration tends to expand
during cooling process in the step (e). At this time, when a site with a
low TiO2 concentration is present adjacent to the site with a high
TiO2 concentration, expansion of the site with a high TiO2
concentration is inhibited, and a compression stress is added. As a
result, a stress distribution is generated in the TiO2--SiO2
glass body. Hereinafter, in the present description, such a stress
distribution is referred to as a "stress distribution caused by striae".

[0084] When a stress distribution caused by striae is present in a
TiO2--SiO2 glass body used as a substrate for an imprint mold,
a difference is produced in processing rate at the time of
finish-processing the surface, and this affects smoothness of the surface
after the finish processing.

[0085] By performing the step (d'), the stress distribution due to striae
in the TiO2--SiO2 glass body produced through the subsequent
step (e) is reduced to a level bringing about no problem in use as a
substrate for an imprint mold.

[0086] The heating temperature in the step (d') is preferably lower than
T1+600° C., more preferably lower than T1+550°
C., and still more preferably lower than T1+500° C., from the
standpoint that foaming or sublimation in the TiO2--SiO2 glass
body is suppressed. That is, the heating temperature in the step (d') is
preferably from T1+400° C. to lower than T1+600°
C., more preferably from T1+400° C. to lower than
T1+550° C., and still more preferably from
T1+450° C. to lower than T1+500° C.

[0087] From the standpoint of, for example, balancing the effect of
reducing striae and the yield of TiO2--SiO2 glass body and
reducing the cost, the heating time in the step (d') is preferably 240
hours or less, and more preferably 150 hours or less. Also, in view of
the effect of reducing striae, the heating time is preferably over 24
hours, more preferably over 48 hours, and still more preferably over 96
hours.

[0088] The step (d') and the later-described step (e) may be performed
sequentially or simultaneously. Also, the step (c) and/or the step (d),
and the step (d') may be performed sequentially or simultaneously.
Furthermore, the step (c) or step (d), and the step (e) may be performed
sequentially or simultaneously.

(Step (e))

[0089] The transparent TiO2--SiO2 glass body obtained in the
step (c), the molded TiO2--SiO2 glass body obtained in the step
(d), or the glass body obtained in the step (d') is subjected to an
annealing treatment of heating to a temperature of 1,100° C. or
higher and then, cooling to a temperature of 700° C. or lower at
an average cooling rate of 100° C./hr or lower, whereby the
fictive temperature of the TiO2--SiO2 glass body is controlled.

[0090] In the case of performing the step (c) or step (d) and the step (e)
sequentially or simultaneously, during the cooling process of from the
temperature of 1,100° C. or higher in the step (c) or step (d), an
annealing treatment of cooling the obtained transparent
TiO2--SiO2 glass body or molded TiO2--SiO2 glass body
from 1,100° C. to 700° C. at an average cooling rate of
100° C./hr or lower is performed, whereby the fictive temperature
of the TiO2--SiO2 glass body is controlled.

[0091] The average cooling rate is preferably 10° C./hr or lower,
more preferably 5° C./hr or lower, and still more preferably
2.5° C./hr or lower.

[0092] After cooling to a temperature of 700° C. or lower, the
glass body can be allowed to stand to be cooled. The atmosphere is not
particularly limited.

[0093] In order to eliminate inclusions such as foreign matters and
bubbles from the TiO2--SiO2 glass body obtained in the step
(e), it is crucial to inhibit contamination in the steps (a) to (d)
(particularly, in the step (a)) and furthermore, precisely control the
temperature condition in the steps (b) to (d).

[0094] The above-described steps (a) to (e) are an example showing the
production method of a TiO2--SiO2 glass body when a soot
process is employed in the step (a). In the case of employing a direct
process in the step (a), a transparent TiO2--SiO2 glass body
can be obtained directly without performing the step (b) and the step
(c). The direct process is a process of obtaining a transparent
TiO2--SiO2 glass body directly by hydrolyzing/oxidizing an
SiO2 precursor and a TiO2 precursor each serving as a
glass-forming raw material, in oxyhydrogen flame at 1,800 to
2,000° C. Subsequently to the step (a) by the direct process, the
step (d) and the step (e) may be sequentially performed. Also, the
transparent TiO2--SiO2 glass body obtained by the direct
process in the step (a) may be cut into a predetermined dimension to
obtain a molded TiO2--SiO2 glass body, and thereafter, the step
(e) may be performed. The transparent TiO2--SiO2 glass body
obtained by the direct process in the step (a) contains H2 or OH. By
adjusting the flame temperature or gas concentration in the direct
process, the OH concentration in the transparent TiO2--SiO2
glass body can be controlled. The OH concentration in the transparent
TiO2--SiO2 glass body can be also controlled by a method of
holding the transparent TiO2--SiO2 glass body obtained by the
direct process in the step (a), in a vacuum, in a reduced pressure
atmosphere, or in the case of normal pressure, in an atmosphere having an
H2 concentration of 1,000 ppm by volume or less and an O2
concentration of 18 vol % or less, at a temperature of 700 to
1,800° C. for 10 minutes to 90 days, thereby achieving degassing.

(Step (f))

[0095] The TiO2--SiO2 glass body obtained in the step (e) is
subjected to machining such as cutting, shaving and polishing, whereby a
TiO2--SiO2 glass substrate having a predetermined shape is
obtained. In the step (f), at least polishing is preferably performed.

[0096] The polishing step is preferably performed in parts in two or more
steps depending on the finished condition of the polished surface. Also,
in two or more polishing steps, it is preferred to properly use at least
two or more kinds of polishing pads of a polyurethane foam-based pad, a
nonwoven fabric-based pad and a suede-based pad. In the final polishing
step, a polishing slurry using colloidal silica is preferably used.

(Step (g))

[0097] The affected layer on the surface of the TiO2--SiO2 glass
substrate obtained in the step (f) is removed, whereby a
TiO2--SiO2 glass substrate is obtained.

[0098] Usually, an affected layer is present on the surface of a glass
substrate finished by machining such as polishing. In the case of forming
a transfer pattern through etching on the surface of the glass substrate
having on the surface thereof such an affected layer, a variation is
liable to occur in etching rate. That is, the etching rate is high in the
affected layer and even when the fictive temperature distribution of the
glass body is made uniform by a heat treatment, a variation in etching
rate due to the affected layer produced by machining liable to occur at
the time of forming a transfer pattern. For preventing this problem, it
is effective to remove the surface by a method except for machining such
as polishing. In the present invention, removal of the affected layer by
an etching treatment is particularly effective. Among the methods for
removing the surface, from the standpoint of maintaining smoothness of
the surface, a method by a chemical etching treatment using a chemical
solution is preferred, a method by immersion in a fluorine-containing
chemical solution is more preferred, and a method by immersion in a
chemical solution containing a hydrofluoric acid is still more preferred.

[0099] In the step (g), the region from the surface to a depth of 100 nm
or more on the side to be subjected to a transfer pattern formation of
the TiO2--SiO2 glass substrate is preferably removed. When the
removal amount by the etching treatment is 100 nm or more, the effect of
the etching treatment is sufficiently exerted. The removal amount by the
etching treatment is more preferably 200 nm or more and still more
preferably 500 nm or more, from the surface. Also, the removal amount by
the etching treatment is preferably less than 10 μm, more preferably
less than 3 μm, still more preferably less than 2 μm, and
particularly preferably less than 1 μm, from the surface. When the
removal amount by the etching treatment is less than 10 μm, reduction
in smoothness of the surface can be suppressed.

[0100] In the case where smoothness of the surface is reduced, mechanical
polishing using a polishing slurry at a low surface pressure (from 1 to
60 gf/cm2), which is called touch polishing, may be performed after
the etching treatment. In the touch polishing, the glass substrate is set
by sandwiching it between polishing plates each provided with a polishing
pad made of nonwoven fabric, abrasive cloth or the like, and the
polishing plates are relatively rotated against the glass substrate while
feeding a slurry adjusted to predetermined properties, whereby the
processing surface is polished at a surface pressure of 1 to 60
gf/cm2. However, an affected layer is also produced by touch
polishing and therefore, an etching treatment is preferably again
performed after the touch polishing.

(Stress)

[0101] The standard deviation (dev[σ]) of stress caused by striae of
the silica-based glass substrate obtained in the step (g) is preferably
0.05 MPa or lower, more preferably 0.04 MPa or lower, and still more
preferably 0.03 MPa or lower. The glass body produced by a soot process
is usually striae-free in three directions, and striae are not observed
therein. However, even a glass body produced by a soot process, in the
case of containing a dopant, there is a possibility that striae may be
observed. If striae are present, a smooth surface is hardly obtained.
Also, for the same reason, the difference (Ac) between the maximum value
and the minimum vale of the stress caused by striae of the silica-based
glass substrate obtained in the step (g) is preferably 0.25 MPa or less,
more preferably 0.2 MPa or less, and still more preferably 0.15 MPa or
less.

[0102] The stress is determined by the following method.

[0103] First, a region of approximately 1 mm×1 mm is measured by
using a birefringent microscope to determine a retardation of the sample,
and the stress profile is determined according to the following formula
(3):

Δ=C×F×n×d (3)

wherein Δ is the retardation, C is photoelastic constant, F is
stress, n is refractive index, and d is the sample thickness.

[0104] From the stress profile, the standard deviation (dev[σ]), and
the difference (Δσ) between the maximum value and the minimum
value of the stress are determined.

[0105] Specifically, a sample is cut out by slicing from a silica-based
glass substrate and then polished to obtain a plate-shaped sample of 30
mm×30 mm×0.5 mm. Using a birefringent microscope, helium neon
laser light is vertically applied onto the plane of 30 mm×30 mm of
the sample, and the in-plane retardation distribution is examined at an
enlarging magnification high enough to enable adequate observation of
striae and converted into a stress distribution. In the case where the
pitch of striae is fine, the thickness of the sample must be made
thinner.

(Function and Effect)

[0106] In the method for producing a silica-based glass substrate of the
present invention described above, the affected layer on the surface of
the glass substrate is removed, so that a silica-based glass substrate
for an imprint mold, where the fictive temperature distribution in the
region from the surface to a depth of 10 μm on the side to be
subjected to a transfer pattern formation is within ±30° C.,
can be obtained. For the following reason, in this silica-based glass
substrate, a transfer pattern with high dimensional accuracy can be
stably formed.

[0107] That is, the present inventors have found that the increase in
dimensional variation at the time of forming a transfer pattern through
etching on a surface of a conventional silica-based glass substrate is
caused by an affected layer produced by machining such as polishing. The
etching rate in the affected layer is high as compared with that in other
portions, as a result, variation arises in etching rate at the time of
forming a transfer pattern through etching and also arises in dimension
(particularly, the dimension in the height direction) of the transfer
pattern formed by etching, and therefore, dimensional accuracy of the
transfer pattern is reduced.

[0108] The affected layer has a high density and in the case of a
silica-based glass substrate, this layer cannot be distinguished from a
portion having a high fictive temperature.

[0109] Accordingly, in the silica-based glass substrate from which the
affected layer has been removed, and which is obtained by the production
method of the present invention, the fictive temperature distribution in
the surface on the side to be subjected to a transfer pattern formation
as well as in the region near the surface is very small. On this account,
in the silica-based glass substrate obtained by the production method of
the present invention, occurrence of variation in etching rate can be
suppressed at the time of forming a transfer pattern through etching, and
a transfer pattern with high dimensional accuracy, for example, a
transfer pattern having a dimensional variation (particularly, a
dimensional variation in the height direction) of preferably ±10% or
less and more preferably ±5% or less, can be formed.

[0110] For this reason, it is suitable as a substrate for an imprint mold,
particularly a substrate for a photo-imprint mold.

[0111] Also, in the case where the silica-based glass substrate obtained
by the production method of the present invention is composed of a
TiO2--SiO2 glass, the thermal expansion coefficient in the
temperature range capable of being experienced by an imprint mold during
imprint lithography (in the case of photo-imprint lithography, near room
temperature (however, the temperature of the mold substrate may arise by
ultraviolet irradiation); and in the case of heat-cycle imprint
lithography, in a temperature range from near room temperature to the
curing temperature of a thermosetting resin) is small. For this reason,
the silica-based glass substrate obtained by the production method of the
present invention, when composed of a TiO2--SiO2 glass, is
excellent in the dimensional stability against a temperature change
capable of being experienced by an imprint mold during imprint
lithography, and therefore is suitable as a substrate for an imprint
mold.

(Fictive Temperature Distribution)

[0112] In the silica-based glass substrate obtained by the production
method of the present invention, the fictive temperature distribution in
the region from the surface to a depth of 10 μm on the side to be
subjected to a transfer pattern formation is within ±30° C.,
and the fictive temperature distribution is preferably within
±20° C., and the fictive temperature distribution is more
preferably within ±10° C. When the fictive temperature
distribution is within ±30° C., the variation in etching rate
at the time of forming a transfer pattern through etching on the surface
of the silica-based glass substrate can be reduced.

[0113] The fictive temperature is determined by the following method.

[0114] (i) A sample whose fictive temperature is unknown is prepared. This
sample is a mirror-polished glass body or a silica-based glass substrate
obtained by etching the surface of the glass body above.

[0115] (ii) A plurality of kinds of glass bodies differing in the fictive
temperature, each of which is a glass body having a known fictive
temperature and having the same composition as the sample above, are
prepared. The surfaces of the glass bodies are previously
mirror-polished.

[0116] (iii) The infrared reflection spectrum on the surface of each of
the glass bodies of (ii) is obtained by using an infrared spectrometer
(Magna 760, manufactured by Nikolet Company). The reflection spectrum is
the average value obtained by scanning 256 times. In the obtained
infrared reflection spectrum, a peak observed in the vicinity of about
1,120 cm-1 is a peak attributed to stretching vibration by an
Si--O--Si bond of the glass, and the peak position depends on the fictive
temperature. A calibration curve showing the relationship between the
peak position and the fictive temperature, obtained with the plurality of
kinds of glass bodies differing in the fictive temperature, is prepared.

[0117] (iv) An infrared reflection spectrum of the sample of (i) is
obtained under the same conditions as in (iii). In the obtained infrared
reflection spectrum, the position of a peak observed in the vicinity of
about 1,120 cm-1, which is attributed to stretching vibration by an
Si--O--Si bond, is exactly determined. The fictive temperature is
determined by comparing this peak position with the calibration curve.

[0118] Also, the fictive temperature distribution in the region from the
surface to a depth of 10 μm is determined as follows.

[0119] First, the fictive temperature of the surface is determined by the
method above. Subsequently, the glass body is immersed in a 10 mass %
hydrofluoric acid solution for 30 seconds to 1 minute, and the mass
decrease between before and after immersion is determined. From the mass
decrease, the etched depth is determined according to the following
formula (4):

(Etched depth)=(mass decrease)/((density)×(surface area)) (4)

[0120] The fictive temperature of the surface exposed after the etching is
also determined by the method above and is taken as the fictive
temperature at that depth. Thereafter, the glass body is again immersed
in a 10 mass % hydrofluoric solution for 30 seconds to 1 minute, and the
depth and the fictive temperature are determined. By repeating this
operation, the maximum value and the minimum value out of the fictive
temperature values obtained by operations immediately before the depth
exceeds 10 μm are determined, and the difference therebetween is taken
as the fictive temperature distribution in the region from the surface to
a depth of 10 μm.

(TiO2--SiO2 Glass)

[0121] The silica-based glass is preferably a TiO2-containing silica
glass (hereinafter, referred to as TiO2--SiO2 glass) containing
TiO2 as a dopant, because a silica-based glass having a low thermal
expansion coefficient and excellent dimensional stability can be
obtained.

[0122] The TiO2 concentration in the TiO2--SiO2 glass (100
mass %) is preferably from 3 to 12 mass %. The silica-based glass
substrate obtained by the production method of the present invention is
used as a substrate for an imprint mold and therefore, is required to
have dimensional stability against a temperature change. When the
TiO2 concentration is from 3 to 12 mass %, the thermal expansion
coefficient at near room temperature can be made small. In order to make
the thermal expansion coefficient at near room temperature almost zero,
the TiO2 concentration is more preferably from 5 to 9 mass % and
still more preferably from 6 to 8 mass %.

[0123] The TiO2 concentration is measured by using a fundamental
parameter (FP) method in the fluorescence X-ray analysis.

[0124] The Ti3+ concentration in the TiO2--SiO2 glass (100
mass %) is preferably, on average, 100 ppm by mass or less, more
preferably 70 ppm by mass or less, still more preferably 20 ppm by mass
or less, and particularly preferably 10 ppm by mass or less. The present
inventors have found that the Ti3+ concentration affects the
coloration of TiO2--SiO2 glass, particularly, the internal
transmittance T300-700 per 1 mm of thickness in the wavelength
region of 300 to 700 nm. When the Ti3+ concentration is 100 ppm by
mass or less, brown coloration can be suppressed, and as a result,
reduction in the internal transmittance T300-700 can be suppressed,
leading to good transparency.

[0125] The Ti3+ concentration is determined by the electron spin
resonance (ESR) measurement. The measurement conditions are as follows.

[0126] Frequency: in the vicinity of 9.44 GHz (X-band),

[0127] Output: 4 mW,

[0128] Modulated magnetic field: 100 KHz, 0.2 mT,

[0129] Measurement temperature: room temperature,

[0130] ESR Species integration range: 332 to 368 mT, and

[0131] Sensitivity calibration: conducted at the peak height of
Mn2+/MgO in a given amount.

[0132] In the ESR signal (differential form) where the signal intensity is
taken on the vertical axis and the magnetic field intensity (mT) is taken
on the horizontal axis, a TiO2--SiO2 glass shows a profile
having an anisotropy of g1=1.988, g2=1.946 and g3=1.915.
Usually, Ti3+ in glass is observed around g=1.9 and therefore, those
signals are designated as signals derived from Ti3+. The Ti3+
concentration is obtained by comparing the intensity after double
integrations with the intensity after double integrations of a
corresponding standard sample having a known concentration.

[0133] The ratio (ΔTi3+/Ti3+) of the variation in the
Ti3+ concentration to the average value of the Ti3+
concentration in a TiO2--SiO2 glass is preferably 0.2 or less,
more preferably 0.15 or less, still more preferably 0.1 or less, and
particularly preferably 0.05 or less. When ΔTi3+/Ti3+ is
0.2 or less, coloration and distribution of characteristics, such as
distribution of absorption coefficient, are reduced.

[0134] The ΔTi3+/Ti3+ is determined by the following
method.

[0135] The Ti3+ concentration is measured every 10 mm from end to end
on an arbitrary line passing the center point of the sample surface. The
difference between the maximum value and the minimum value of the
Ti3+ concentration is taken as ΔTi3+ and divided by the
average value of the Ti3+ concentration to determine
ΔTi3+/Ti3+.

(Thermal Expansion Coefficient)

[0136] In the silica-based glass substrate obtained by the production
method of the present invention, the thermal expansion coefficient
C15-35 at 15 to 35° C. is preferably in the range of 0±200
ppb/° C. The silica-based glass substrate obtained by the
production method of the present invention is used as a substrate for an
imprint mold and therefore, is required to be excellent in dimensional
stability against a temperature change, more specifically, excellent in
dimensional stability against a temperature change in the temperature
region capable of being experienced by the mold during imprint
lithography. Here, the temperature region capable of being experienced by
the imprint mold varies depending on the kind of imprint lithography. In
the photo-imprint lithography, a photocurable resin is cured by
ultraviolet irradiation and therefore, the temperature region capable of
being experienced by the mold is fundamentally near room temperature.
However, the temperature of the mold sometimes locally rises due to
ultraviolet irradiation. Considering the local temperature rising due to
ultraviolet irradiation, it is assumed that the temperature region
capable of being experienced by the mold is 15 to 35° C.
C15-35 is more preferably in the range of 0±100 ppb/° C.,
still more preferably in the range of 0±50 ppb/° C., and
particularly preferably in the range of 0±20 ppb/° C.

[0137] In the silica-based glass substrate obtained by the production
method of the present invention, the thermal expansion coefficient
C22 at 22° C. is preferably 0±30 ppb/° C., more
preferably 0±10 ppb/° C., and still more preferably 0±5
ppb/° C. When C22 is in the range of 0±30 ppb/° C.,
the dimensional change due to temperature change can be neglected
regardless of whether the value is positive or negative.

[0138] For achieving accurate measurement with a small number of
measurement points like the thermal expansion coefficient at 22°
C., the dimensional change of a sample due to temperature change by 1 to
3° C. around the temperature is measured by using a laser
heterodyne interferometric thermal expansion meter (for example, a laser
heterodyne interferometric thermal expansion meter, CTE-01, manufactured
by Uniopt), and the average thermal expansion coefficient determined is
taken as the thermal expansion coefficient at the middle temperature.

(Internal Transmittance)

[0139] In the silica-based glass substrate obtained by the production
method of the present invention, the internal transmittance T300-700
per 1 mm of thickness in the wavelength region of 300 to 700 nm is
preferably 70% or more, more preferably 80% or more, still more
preferably 85% or more, and particularly preferably 90% or more.

[0140] In the photo-imprint lithography, a photocurable resin is cured by
ultraviolet irradiation and therefore, the ultraviolet transmittance is
preferably high.

[0141] In the silica-based glass substrate obtained by the production
method of the present invention, the internal transmittance T400-700
per 1 mm of thickness in the wavelength region of 400 to 700 nm is
preferably 80% or more, more preferably 85% or more, and still more
preferably 90% or more. When T400-700 is 80% or more, visible light
is hardly absorbed, as a result, the presence or absence of an internal
defect such as bubble and stria is easily judged at the inspection with a
microscope, an eye or the like, and a problem is less likely to occur in
the inspection or evaluation.

[0142] In the silica-based glass substrate obtained by the production
method of the present invention, the internal transmittance
T300-3000 per 1 mm of thickness in the wavelength region of 300 to
3,000 nm is preferably 70% or more, more preferably 80% or more, still
more preferably 85% or more, and particularly preferably 90% or more. In
the photo-imprint lithography, a photocurable resin is cured by
ultraviolet irradiation and therefore, the ultraviolet transmittance is
preferably high. Also, light absorption in the range of from visible
light region to near infrared light region is suppressed, and a
temperature rise due to light absorption is suppressed.

[0143] The internal transmittance is determined by the following method.

[0144] The transmittance of a sample (a mirror-polished glass substrate or
a silica-based glass substrate obtained by etching the surface of the
glass body above) is measured using a spectrophotometer. The internal
transmittance per 1 mm of thickness is determined by measuring the
transmittance on samples which are subject to polishing in the same level
and different in the thickness, for example, a sample with a thickness of
2 mm and a sample with a thickness of 1 mm, converting each transmittance
into an absorbance, subtracting the absorbance of the sample with a
thickness of 1 mm from the absorbance of the sample with a thickness of 2
mm to obtain an absorbance per 1 mm of thickness, and again converting
the absorbance into a transmittance.

(OH Concentration)

[0145] The OH concentration in the silica-based glass substrate obtained
by the production method of the present invention is preferably less than
600 ppm by mass, more preferably 400 ppm by mass or less, still more
preferably 200 ppm by mass or less, and particularly preferably 100 ppm
by mass or less. When the OH concentration is less than 600 ppm by mass,
reduction in the light transmittance in the near infrared region due to
absorption by the OH group can be suppressed, and T300-3000 hardly
becomes less than 80%.

[0146] The OH concentration is determined by the following method.

[0147] Measurement is performed by means of an infrared spectrometer, and
the OH concentration is determined from the absorption peak at a
wavelength of 2.7 μm (J. P. Williams, et al., Ceramic Bulletin, 55(5),
524, 1976). The detection limit by this method is 0.1 ppm by mass.

(Fluorine Concentration)

[0148] The silica-based glass substrate obtained by the production method
of the present invention may contain fluorine. In the case of
incorporating F into the TiO2--SiO2, glass substrate for the
purpose of widening the temperature range of zero expansion, the fluorine
concentration is preferably 1,000 ppm by mass or more, more preferably
2,000 ppm by mass or more, still more preferably 3,000 ppm by mass or
more, and particularly preferably 4,000 ppm by mass or more. In the case
of the purpose of simply reducing the OH concentration, the fluorine
concentration is preferably 100 ppm by mass or more, more preferably 200
ppm by mass or more, and still more preferably 500 ppm by mass or more.

(Halogen Concentration Other than Fluorine)

[0149] In the silica-based glass substrate obtained by the production
method of the present invention, the halogen concentration other than
fluorine is preferably less than 50 ppm by mass, more preferably 20 ppm
by mass or less, still more preferably 1 ppm by mass or less, and
particularly preferably 0.1 ppm by mass or less. When the halogen
concentration other than fluorine is less than 50 ppm by mass, the
Ti3+ concentration is hardly increased and therefore, brown
coloration is less likely to occur. As a result, reduction in the
transmittance is suppressed, and the transparency is hardly impaired.

[0150] The halogen concentration is determined by the following method.

[0151] The sample is heated and dissolved in a sodium hydroxide solution,
and filtered through a cation removing filter. And then the resulting
solution is quantitatively analyzed for the chlorine ion concentration by
ion chromatograph analysis, whereby the chlorine concentration is
determined.

[0152] The fluorine concentration is determined by a fluorine ion
electrode method. Specifically, in accordance with the method disclosed
in Journal of Chemical Society of Japan, 1972 (2), 350, the sample is
heated and melted in anhydrous sodium carbonate, and to the obtained
melt, distilled water and hydrochloric acid (in a volume ratio of 1:1)
are added, whereby a sample solution is prepared. The electromotive force
of the sample solution is measured by a radiometer by using No. 945-220
and No. 945-468, both are manufactured by Radiometer Trading, as a
fluorine ion selective electrode and a comparative electrode,
respectively, and the fluorine concentration is determined based on a
calibration curve preliminarily created by using fluorine ion standard
solutions.

[0153] Other halogen concentrations can be determined by a known method,
for example, by ion chromatograph analysis.

<Imprint Mold>

[0154] In the present invention, the imprint mold is produced by forming a
transfer pattern through etching on a surface of the silica-based glass
substrate obtained by the production method of the present invention.

[0155] The transfer pattern is a reversed pattern of the target fine
concave-convex pattern and consists of a plurality of fine convexes
and/or concaves.

[0156] Examples of the convex include a long linear convex extending on
the surface of the imprint mold, and protrusions scattered on the
surface.

[0157] Examples of the concave include a long groove extending in the
surface of the imprint mold, and holes scattered in the surface.

[0158] Examples of the shape of the linear convex or groove include a
straight line, a curved line, and a bent line. A plurality of linear
convexes or grooves may be present in parallel to make a stripe pattern.

[0159] Examples of the cross-sectional shape in the direction orthogonal
to the longitudinal direction of the linear convex or groove include a
rectangle, a trapezoid, a triangle, and a semicircle.

[0160] Examples of the shape of the protrusion or hole include a
triangular prism, a quadrangular prism, a hexagonal prism, a circular
cylinder, a triangular cone, a quadrangular cone, a hexagonal cone, a
circular cone, a hemisphere, and a polyhedron.

[0161] The width of the linear convex or groove is, on average, preferably
from 1 nm to 500 μm, more preferably from 10 nm to 100 μm, and
still more preferably from 15 nm to 10 μm. The width of the linear
convex means the length of the base in the cross-section in the direction
orthogonal to the longitudinal direction. The width of the groove means
the length of the top in the cross-section in the direction orthogonal to
the longitudinal direction.

[0162] The width of the protrusion or hole is, on average, preferably from
1 nm to 500 μm, more preferably from 10 nm to 100 μm, and still
more preferably from 15 nm to 10 μm. The width of the protrusion
means, in the case of a long and thin bottom, the length of the base in
the cross-section in the direction orthogonal to the longitudinal
direction, and, otherwise, the maximum length in the bottom of the
protrusion. The width of the hole means, in the case of a long and thin
opening, the length of the top in the cross-section in the direction
orthogonal to the longitudinal direction, and, otherwise, the maximum
length in the opening of the hole.

[0163] The height of the convex is, on average, preferably from 1 nm to
500 μm, more preferably from 10 nm to 100 μm, and still more
preferably from 15 nm to 10 m.

[0164] The depth of the concave is, on average, preferably from 1 nm to
500 μm, more preferably from 10 nm to 100 μm, and still more
preferably from 15 nm to 10 μm.

[0165] In the region where the transfer pattern is densely formed, the
distance between adjacent convexes (or concaves) is, on average,
preferably from 1 nm to 500 μm, and more preferably from 1 nm to 50
μm. The distance between adjacent convexes means the distance from the
end of the base in the cross-section of a convex to the beginning of the
base in the cross-section of the adjacent convex. The distance between
adjacent concaves means the distance from the end of the top in the
cross-section of a convex to the beginning of the top in the
cross-section of the adjacent concave.

[0166] The minimum dimension of the convex is preferably from 1 nm to 50
μm, more preferably from 1 nm to 500 nm, and still more preferably
from 1 nm to 50 nm. The minimum dimension means the minimum dimension out
of the width, the length and the height of the convex.

[0167] The minimum dimension of the concave is preferably from 1 nm to 50
μm, more preferably from 1 nm to 500 nm, and still more preferably
from 1 nm to 50 nm. The minimum dimension means the minimum dimension out
of the width, the length and the depth of the concave.

<Method for Producing Imprint Mold>

[0168] The method for producing an imprint mold of the present invention
is a method of forming a transfer pattern through etching on a surface of
the silica-based glass substrate obtained by the production method of the
present invention.

[0170] In the above-described method for producing an imprint mold of the
present invention, since a transfer pattern is formed by etching on a
surface of the silica-based glass substrate obtained by the production
method of the present invention, an imprint mold having a transfer
pattern with high dimensional accuracy is obtained.

EXAMPLES

[0171] The present invention is described in greater detail below by
referring to Examples, but the present invention is not limited thereto.

[0172] Examples 1 to 3 are Production Examples, Examples 4 to 6 and 9 are
Inventive Examples, and Examples 7 and 8 are Comparative Examples.

Example 1

Step (a)

[0173] A TiO2--SiO2 glass fine particle obtained by mixing
TiCl4 and SiCl4 as glass-forming raw materials each after
gasification, and heating and hydrolyzing (flame-hydrolyzing) the mixed
gas in oxyhydrogen flame was deposited and grown on a substrate for
deposition to form a porous TiO2--SiO2 glass body.

[0174] The obtained porous TiO2--SiO2 glass body was difficult
to handle without any treatment, and therefore, the glass body was held
at 1,200° C. for 4 hours in the air in the state of being still
deposited on the substrate for deposition and then removed from the
substrate for deposition.

Step (b)

[0175] Thereafter, the porous TiO2--SiO2 glass body was held at
1,450° C. for 4 hours under reduced pressure to obtain a
TiO2--SiO2 dense body.

Step (c)

[0176] The obtained TiO2--SiO2 dense body was put in a carbon
mold and held at 1,680° C. for 4 hours in an argon atmosphere
under atmospheric pressure to obtain a transparent TiO2--SiO2
glass body.

Step (d)

[0177] The obtained transparent TiO2--SiO2 glass body was put in
a carbon mold and held at 1,700° C. for 4 hours in an argon
atmosphere under atmospheric pressure, thereby performing molding, to
obtain a molded TiO2--SiO2 glass body.

Steps (d') to (e)

[0178] The obtained molded TiO2--SiO2 glass body was held at
1,590° C. for 120 hours in an argon atmosphere under atmospheric
pressure (step (d')).

[0179] Subsequently, the glass body was cooled to 1,000° C. at
10° C./hr, held at 1,000° C. for 3 hours, cooled to
950° C. at 10° C./hr, held at 950° C. for 72 hours,
cooled to 900° C. at 5° C./hr, held at 900° C. for
72 hours, and cooled to room temperature to obtain a TiO2--SiO2
glass body (step (e)). The average cooling rate from 1,100° C. to
700° C. in the step (e) was 2.3° C./hr.

Example 2

Step (a)

[0180] A TiO2--SiO2 glass fine particle obtained by mixing
TiCl4 and SiCl4 as glass-forming raw materials each after
gasification, and heating and hydrolyzing (flame hydrolyzing) the mixed
gas in oxyhydrogen flame was deposited and grown on a substrate for
deposition to form a porous TiO2--SiO2 glass body.

[0181] The obtained porous TiO2--SiO2 glass body was difficult
to handle without any treatment, and therefore, the glass body was held
at 1,200° C. for 4 hours in the air in the state of being still
deposited on the substrate for deposition and then removed from the
substrate for deposition.

Step (b)

[0182] Thereafter, the porous TiO2--SiO2 glass body was
supported on a PFA (perfluoroalkoxyalkane)-made jig and together with the
jig, put in a nickel-made autoclave (A/C). Subsequently, an NaF pellet
(produced by Stella Chemifa Corporation) was inserted into the autoclave
while keeping the pellet from contacting with the porous
TiO2--SiO2 glass body, and the autoclave was externally heated
by using an oil bath to heat to a temperature of 80° C.

[0183] While keeping the inside of the autoclave at 80° C., vacuum
deaeration was performed until the pressure in the autoclave reached an
absolute pressure of 266 Pa or lower, and the system was held for one
hour.

[0184] Furthermore, a gas of elemental fluorine (F2) diluted with a
nitrogen gas to 20 vol % was introduced until the pressure in the
apparatus reached a gauge pressure of 0.18 MPa, and after heating to
80° C., the system was held for 24 hours, whereby fluorine was
introduced into the porous TiO2--SiO2 glass body. The glass
body was then held at 1,450° C. for 4 hours under reduced pressure
to obtain a TiO2--SiO2 dense body.

Step (c)

[0185] The obtained TiO2--SiO2 dense body was put in a carbon
mold and held at 1,680° C. for 4 hours in an argon atmosphere
under atmospheric pressure to obtain a transparent TiO2--SiO2
glass body.

Step (d)

[0186] The obtained transparent TiO2--SiO2 glass body was put in
a carbon mold and held at 1,700° C. for 4 hours in an argon
atmosphere under atmospheric pressure, thereby performing molding to
obtain a molded TiO2--SiO2 glass body.

Step (e)

[0187] The obtained molded TiO2--SiO2 glass body was heated at
1,200° C., then cooled from 1,200° C. to 500° C. at
5° C./hr in the air and thereafter, allowed to stand to be cooled
to room temperature to obtain a TiO2--SiO2 glass body.

Example 3

[0188] ULE #7972 produced by Corning Incorporated, which is known as a
zero expansion TiO2--SiO2 glass, was held at 900° C. for
100 hours in the air and then quenched to control the fictive
temperature.

[Evaluation]

[0189] With respect to the TiO2--SiO2 glass body obtained in
each of Examples 1 to 3, TiO2 concentration, Ti3+
concentration, ΔTi3+/Ti3+, OH concentration, halogen
concentration, internal transmittance, fictive temperature, stress, and
thermal expansion coefficient were determined by the methods described
above. The results are shown in Table 1 and Table 2. Incidentally, the
fictive temperature is not the distribution but the value of the entire
glass body. Also, the data for the glass body in the section of
[Evaluation] are not changed by the later-described cutting, shaving,
polishing and etching treatments in the section of [Examples 4 to 9].

[0190] The TiO2--SiO2 glass body obtained in each of Examples 1
to 3 is cut into a plate shape of length of about 153.0 mm×width of
about 153.0 mm×thickness of about 6.75 mm by using an
inner-diameter saw slicer and then chamfered to obtain a plate material
of length of about 153.0 mm×width of about 153.0 mm×thickness
of about 6.7 mm. Thereafter, using 20B double-side lapper (manufactured
by SPEEDFAM Co., Ltd.), the main surface (surface on which a transfer
pattern is to be formed) of the plate material is shaved with a slurry
obtained by suspending from 18 to 20 mass % of an abrasive substantially
composed of Al2O3 (AZ #1000 manufactured by HEISEI SANKEI Co.,
Ltd.) in filtrated water, until the thickness becomes about 6.5 mm. Then,
the end face is mirror-processed.

[0191] Subsequently, as a first polishing step, the main surface of the
plate material is polished about 50 μm by using the 20B double-side
polisher with a foamed polyurethane-made polishing pad and an abrasive
containing cerium oxide as a main component.

[0192] Furthermore, as a second polishing step, the main surface of the
plate material is polished about 15 μm by using a 24B double-side
polisher with a suede-based polishing pad in which an NAP layer is formed
on nonwoven fabric bonded by polyurethane and which is a polishing pad
coming under 68 in ASKER C in accordance with the Society of Rubber
Industry, Japan Standard (SRIS), and an abrasive containing cerium oxide
as a main component.

[0193] In addition, a third polishing step is performed by a different
polishing machine. In this third polishing step, a suede-based polishing
pad in which an NAP layer is formed on a PET sheet, and colloidal silica
are used.

[0194] The obtained TiO2--SiO2 glass substrate is immersed in a
10 mass % hydrofluoric acid solution for 30 seconds, and the surface is
thereby etched to obtain a TiO2--SiO2 glass substrate. The
depth of etching can be calculated from the mass decrease and is 0.8
μm. This TiO2--SiO2 glass substrate is measured by the
method above for fictive temperature distribution in the region from the
surface to a depth of 10 μm on the side to be subjected to a transfer
pattern formation, as a result, only a difference within 10° C. is
observed, which is a measurement error in the method of performing
measurement by means of an infrared reflection spectrum.

Example 7

[0195] The TiO2--SiO2 glass body obtained in Example 1 is
subjected to the same polishing as the polishing in the section of
[Examples 4 to 6]. Without performing immersion in a 10 mass %
hydrofluoric acid solution, the polished TiO2--SiO2 glass
substrate is measured by the method above for fictive temperature
distribution in the region from the surface to a depth of 10 μm on the
side to be subjected to a transfer pattern formation, as a result, the
fictive temperature on the outermost surface is higher by 70° C.
than the inside.

Example 8

[0196] The TiO2--SiO2 glass body obtained in Example 1 is
subjected to the same polishing as the polishing in the section of
[Examples 4 to 6], and then, the shape is corrected by a gas cluster ion
beam. Thereafter, the main surface is again finished with a suedebased
polishing pad in which an NAP layer is formed on a PET sheet, and
colloidal silica. This TiO2--SiO2 glass substrate is measured
by the method above for fictive temperature distribution in the region
from the surface to a depth of 10 μm on the side to be subjected to a
transfer pattern formation, as a result, the fictive temperature on the
outermost surface is higher by 350° C. than the inside.

Example 9

[0197] The TiO2--SiO2 glass substrate obtained in Example 8 is
immersed in a 10 mass % hydrofluoric acid solution for one minute to etch
the surface, to thereby obtain a TiO2--SiO2 glass substrate.
The depth of etching can be calculated from the mass decrease and is 1.4
μm. This TiO2--SiO2 glass substrate is measured by the
method above for fictive temperature distribution in the region from the
surface to a depth of 10 μm on the side to be subjected to a transfer
pattern formation, as a result, only a difference within 10° C. is
observed, which is a measurement error in the method of performing
measurement by means of an infrared reflection spectrum.

CONCLUSION

[0198] In the TiO2--SiO2 glass substrate after the etching
treatment of each of Examples 7 and 8, the fictive temperature
distribution in the region from the surface to a depth of 10 μm on the
side to be subjected to a transfer pattern formation is large and
therefore, at the time of forming a transfer pattern (concave-convex
pattern) by etching, a variation occurs in etching rate. As a result,
dimensional accuracy of the transfer pattern is reduced.

[0199] In the TiO2--SiO2 glass substrate of each of Examples 4
to 6 and 9, the fictive temperature distribution in the region from the
surface to a depth of 10 μm on the side to be subjected to a transfer
pattern formation is small and therefore, at the time of forming a
transfer pattern (concave-convex pattern) by etching, a variation hardly
occurs in etching rate. As a result, dimensional accuracy of the transfer
pattern is increased.

[0200] Incidentally, in the TiO2--SiO2 glass substrate of
Example 6, since the OH concentration is high, T300-3000 is small,
and there is a possibility that light absorption may arise as a problem
in use for photo-imprint lithography.

[0201] While the present invention has been described in detail and with
reference to specific embodiments thereof, it will be apparent to one
skilled in the art that various changes and modifications can be made
therein without departing from the spirit and scope of the present
invention.

[0202] This application is based on Japanese Patent Application No.
2009-276314 filed on Dec. 4, 2009, the contents of which are incorporated
herein by way of reference.

INDUSTRIAL APPLICABILITY

[0203] The silica-based glass substrate obtained by the production method
of the present invention is useful as a material for an imprint mold that
is used for the purpose of forming a fine concave-convex pattern with a
dimension of 1 nm to 10 μm in a semiconductor device, an optical
waveguide, a micro-optical element (such as diffraction grating), a
biochip, a microreactor, or the like.